New posts in continuity

Topological spaces in which a set is the support of a continuous function iff it is the closure of a open set.

general-topology continuity

$f$ continuous iff $\operatorname{graph}(f)$ is compact

general-topology continuity compactness

Limit with integral or is this function continuous?

integration limits multivariable-calculus continuity

Path Connectedness and continuous bijections

general-topology continuity connectedness abstract-algebra

Verifying continuity of the deformation retraction of the mapping cylinder

general-topology algebraic-topology continuity

Separation in compact spaces

real-analysis general-topology proof-verification continuity

Continuously extending a set of independent vectors to a basis.

linear-algebra general-topology continuity

What is the difference between the terms smooth, analytical and continuous?

continuity analyticity smooth-manifolds

Handoff webpages in Safari from iPhone to MacBook without the Dock

macos iphone safari mojave continuity

$f$ is uniformly continuity

real-analysis continuity uniform-continuity

Why "a function continuous at only one point" is not an oxymoron?

real-analysis continuity

Construction of a continuous function which is not bounded on given interval.

real-analysis continuity

On continuity of roots of a polynomial depending on a real parameter

real-analysis complex-analysis algebraic-topology continuity

Why differentiability implies continuity, but continuity does not imply differentiability?

real-analysis derivatives continuity examples-counterexamples

Proving f is a Lipschitz continuous function. (Real analysis)

real-analysis continuity

Is there a function $f(x)$ that satisfies $f(e^x) = e^x f(x)$?

partial-differential-equations continuity functional-equations

$g(x)$ is continuous on $\mathbb{R}$ st $g(x)=g(x^2)$. Prove that $g(x)$ is constant.

real-analysis continuity

A continuous function that maps closed unit square to the unit open square

real-analysis general-topology continuity metric-spaces solution-verification

if $f(x + y) = f(x)f(y)$ is continuous, then it has to be injective.

functions continuity exponential-function functional-equations

I want to find A real valued function having a continuous first derivative for all points in domain, but with undefined higher order derivatives.

real-analysis continuity